Question

Show if the series $f(x)=\sum\limits_{k=1}^\infty \frac{1}{k} \sin(\frac{x}{k})$ converges uniformly or not.

score 3.1k · Answer 1 · 2014-06-29 14:51:55

3.1k

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Show if the series $f(x)=\sum\limits_{k=1}^\infty \frac{1}{k} \sin(\frac{x}{k})$ converges uniformly or not.

Published on 29 Jun 2014 - 14:51

score 2.3k · Answer 2 · 2014-06-30 22:53:53

2.3k

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Uniform convergence of $f^2_n$ when $f_n$ converges uniformly

Published on 30 Jun 2014 - 22:53

score 82 · Answer 3 · 2014-07-05 09:08:52

82

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It is a question about uniform convergence of a function.

Published on 05 Jul 2014 - 9:08

score 3.7k · Answer 4 · 2014-07-06 10:32:41

3.7k

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How to show that $f_n(x) = \frac{1}{1+nx^2}$ on $\mathbb{R}$ is not uniformly convergent

Published on 06 Jul 2014 - 10:32

score 1.8k · Answer 5 · 2026-03-31 11:08:43

1.8k

Views

A counter-example to Dini's Theorem (after removing a hypothesis)

Published on 31 Mar 2026 - 11:08

score 69 · Answer 6 · 2014-07-10 09:37:31

69

Views

Show that $\lim_{s \to \infty}F_s(t) = F(t)$ uniformly for $t \in (0,+\infty)$

Published on 10 Jul 2014 - 9:37

score 248 · Answer 7 · 2014-07-14 01:59:02

248

Views

Uniform convergence result in proof of second-derivative formula

Published on 14 Jul 2014 - 1:59

score 162 · Answer 8 · 2014-07-21 17:05:26

162

Views

Uniform Convergence and Sup

Published on 21 Jul 2014 - 17:05

score 149 · Answer 9 · 2026-04-02 10:04:07

149

Views

Are the family of given nice functions $f\subset C^0(I,[0,1])$ equicontinuous?

Published on 02 Apr 2026 - 10:04

score 74 · Answer 10 · 2014-07-23 20:23:08

74

Views

Let $f_n(x)=x^n$ on $I=[0,1)$, does $\sum\limits_{n=1}^\infty f_n(x)$?

Published on 23 Jul 2014 - 20:23

score 266 · Answer 11 · 2014-07-24 21:16:08

266

Views

If $f_n(t):=f(t^n)$ converges uniformly to continuous function then $f$ constant

Published on 24 Jul 2014 - 21:16

score 159 · Answer 12 · 2014-07-25 22:02:50

159

Views

Non stationary solutions of the PDE $u_t + u_x = u_{xx}$

Published on 25 Jul 2014 - 22:02

score 2k · Answer 13 · 2014-07-26 17:21:37

2k

Views

Prove if $f_n(x)=n^2 x^n(1-x)^2$ converges pointwise and/or uniformly on $I=[0,a]$, where $a<1$

Published on 26 Jul 2014 - 17:21

score 829 · Answer 14 · 2014-07-29 07:46:46

829

Views

Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism

Published on 29 Jul 2014 - 7:46

score 1.5k · Answer 15 · 2026-04-02 10:07:39

1.5k

Views

Uniform convergence on compact sets allows switching the limit and the integral.

Published on 02 Apr 2026 - 10:07

List Question

Show if the series $f(x)=\sum\limits_{k=1}^\infty \frac{1}{k} \sin(\frac{x}{k})$ converges uniformly or not.

Uniform convergence of $f^2_n$ when $f_n$ converges uniformly

It is a question about uniform convergence of a function.

How to show that $f_n(x) = \frac{1}{1+nx^2}$ on $\mathbb{R}$ is not uniformly convergent

A counter-example to Dini's Theorem (after removing a hypothesis)

Show that $\lim_{s \to \infty}F_s(t) = F(t)$ uniformly for $t \in (0,+\infty)$

Uniform convergence result in proof of second-derivative formula

Uniform Convergence and Sup

Are the family of given nice functions $f\subset C^0(I,[0,1])$ equicontinuous?

Let $f_n(x)=x^n$ on $I=[0,1)$, does $\sum\limits_{n=1}^\infty f_n(x)$?

If $f_n(t):=f(t^n)$ converges uniformly to continuous function then $f$ constant

Non stationary solutions of the PDE $u_t + u_x = u_{xx}$

Prove if $f_n(x)=n^2 x^n(1-x)^2$ converges pointwise and/or uniformly on $I=[0,a]$, where $a<1$

Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism

Uniform convergence on compact sets allows switching the limit and the integral.

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